The goal of this proposal is to develop statistical methods and algorithms for the design and analysis of multi-drug combination studies. Drug combinations are the hallmark of therapies for complex diseases such as cancer, HIV and hypertension. Because drug-effect is dose-dependent, multiple doses of an individual drug need to be examined, yielding rapidly rising number of combinations and a challenging high dimensional statistical problem. The lack of proper design and analysis methods for multi-drug combination studies have resulted in many missed therapeutic opportunities. Our preliminary studies have identified an analytic formula for determining the relative potency of two anticancer drugs, which contradicts the common assumption of constant relative potency in the field. Furthermore, we have developed a maximal power approach for the design and analysis of combination studies so that the statistical power to detect departures from additively is maximized, the dose-response can be estimated with moderate sample size. Currently multi-drug combination studies have to resort to suboptimal design such as pair wise evaluation of two-drugs. We propose a novel two-stage procedure starting with an initial selection by utilizing an in silico model built upon experimental data of single drugs in conjunction with available network or pathway information and followed with efficient experimental designs on selected multi-drug combinations and statistical analysis of the data. Integrating modern statistical methods, mathematics, pharmacology and computing, we propose to (1) develop the statistical models and algorithms for the optimal selection of drugs and their interactions utilizing single-drug dose response data and signaling pathway/network information; (2) develop experimental designs and statistical analysis for characterizing dose-responses using the in silico results in Aim 1; (3) develop statistical methods for the interaction (synergy) analysis of multi-drug combinations, (4) test the methods in cancer cell lines in studies already funded by NCI, and other funding agencies; and (5) enrich computer programs developed in Aims 1-3. Upon completion of the project, it is anticipated that the method will be able to serve a much larger translational research community and it will also have bearing to statistical research dealing with high dimensional data.